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<p>Missing data is a common problem in statistical analysis. When a variable has missing values, the multiply robust method to estimate the population mean was developed to ensure that the estimation is robust against model misspecification. It provides a consistent estimator if one of the propensity models and imputation models is correctly specified. Moreover, the multiply robust estimator is semiparametrically efficient if one of the propensity models and one of the imputation models are correctly specified. The multiply robust estimation method was developed based on the empirical likelihood and calibration methods. Various distance functions are used to estimate the parameter in the generalized empirical likelihood and calibration methods; however, only a specific distance function can be used in the multiply robust estimation method. This paper develops a multiply robust method using various distance functions to estimate population means. The proposed method provides a consistent estimator if one of the propensity models and imputation models is correctly specified, and a semiparametrically efficient estimator if one of the propensity models and one of the imputation models are correctly specified.</p>

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On distance functions in multiply robust estimation of population means

  • 期刊论文

  • 发表日期：

    2026年1月17日

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  • Tadayoshi Fushiki

摘要

Missing data is a common problem in statistical analysis. When a variable has missing values, the multiply robust method to estimate the population mean was developed to ensure that the estimation is robust against model misspecification. It provides a consistent estimator if one of the propensity models and imputation models is correctly specified. Moreover, the multiply robust estimator is semiparametrically efficient if one of the propensity models and one of the imputation models are correctly specified. The multiply robust estimation method was developed based on the empirical likelihood and calibration methods. Various distance functions are used to estimate the parameter in the generalized empirical likelihood and calibration methods; however, only a specific distance function can be used in the multiply robust estimation method. This paper develops a multiply robust method using various distance functions to estimate population means. The proposed method provides a consistent estimator if one of the propensity models and imputation models is correctly specified, and a semiparametrically efficient estimator if one of the propensity models and one of the imputation models are correctly specified.